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Power, Selection Bias and Predictive Performance of the Population Pharmacokinetic Covariate Model
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences, Division of Pharmacokinetics and Drug Therapy.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences, Division of Pharmacokinetics and Drug Therapy.
2004 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 31, no 2, 109-134 p.Article in journal (Refereed) Published
Abstract [en]

Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).

Place, publisher, year, edition, pages
2004. Vol. 31, no 2, 109-134 p.
National Category
Medical and Health Sciences
URN: urn:nbn:se:uu:diva-95982PubMedID: 15379381OAI: oai:DiVA.org:uu-95982DiVA: diva2:170383
Available from: 2007-05-15 Created: 2007-05-15 Last updated: 2016-03-24Bibliographically approved
In thesis
1. Covariate Model Building in Nonlinear Mixed Effects Models
Open this publication in new window or tab >>Covariate Model Building in Nonlinear Mixed Effects Models
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Population pharmacokinetic-pharmacodynamic (PK-PD) models can be fitted using nonlinear mixed effects modelling (NONMEM). This is an efficient way of learning about drugs and diseases from data collected in clinical trials. Identifying covariates which explain differences between patients is important to discover patient subpopulations at risk of sub-therapeutic or toxic effects and for treatment individualization. Stepwise covariate modelling (SCM) is commonly used to this end. The aim of the current thesis work was to evaluate SCM and to develop alternative approaches. A further aim was to develop a mechanistic PK-PD model describing fasting plasma glucose, fasting insulin, insulin sensitivity and beta-cell mass.

The lasso is a penalized estimation method performing covariate selection simultaneously to shrinkage estimation. The lasso was implemented within NONMEM as an alternative to SCM and is discussed in comparison with that method. Further, various ways of incorporating information and propagating knowledge from previous studies into an analysis were investigated. In order to compare the different approaches, investigations were made under varying, replicated conditions. In the course of the investigations, more than one million NONMEM analyses were performed on simulated data. Due to selection bias the use of SCM performed poorly when analysing small datasets or rare subgroups. In these situations, the lasso method in NONMEM performed better, was faster, and additionally validated the covariate model. Alternatively, the performance of SCM can be improved by propagating knowledge or incorporating information from previously analysed studies and by population optimal design.

A model was also developed on a physiological/mechanistic basis to fit data from three phase II/III studies on the investigational drug, tesaglitazar. This model described fasting glucose and insulin levels well, despite heterogeneous patient groups ranging from non-diabetic insulin resistant subjects to patients with advanced diabetes. The model predictions of beta-cell mass and insulin sensitivity were well in agreement with values in the literature.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2007. 77 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 59
Pharmacokinetics/Pharmacotherapy, Pharmacokinetics, Pharmacodynamics, Modeling, Covariate selection, Stepwise selection, Covariate analysis, Methodology, Model validation, Model evaluation, Type-2 diabetes, Beta-cell function, Meta analysis, Cross-validation, Least absolute shrinkage and selection operator, Pharmacometrics, ED optimization, Farmakokinetik/Farmakoterapi
urn:nbn:se:uu:diva-7923 (URN)978-91-554-6915-3 (ISBN)
Public defence
2007-06-05, B41, BMC, Husarg. 3, Uppsala, 09:15
Available from: 2007-05-15 Created: 2007-05-15 Last updated: 2010-12-09Bibliographically approved

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